You've given me a lot of awesome references and things to think about. I've only just started working through them all. But one question that jumps out to me off the bat is what do you mean by: "the typical difficulty in determination of loss function, convexity is convenient yet concavity is a more faithful description of boundary behavior"? How are convexity/concavity not the same thing in this context?

Hmm... it seems the website won't let me award the bounty for another 24 hours. That's dumb. I hope I don't forget.

Yes, I'm assuming that $k<d$.

This doesn't actually answer the question for me. You haven't used anywhere the random structure of the $W$ matrix, and the final answer is still a function of the particular values of $W$. (Sorry for the delayed response as I've been on vacation.)